Gordon Brown has suffered a devastating collapse in his public standing, according to a new survey published in The Observer today which will put his leadership under intensified pressure.

As the Prime Minister begins his fightback with new proposals entitling mothers to more flexible working hours, the research shows that only one in five voters thinks he is doing a good job. He is rated worse than David Cameron on every key leadership quality, including competence, decisiveness, fairness, likeability, trustworthiness and strength.

A unique opinion tracker using a panel of 5,000 voters, much larger than conventional opinion polls, reveals that he is floundering in his attempt to campaign for public respect after Labour's large losses in the council elections. Three-quarters think he is doing a bad job, and nearly half of them believe he is doing a very bad job, according to the first results from the survey, which was published on the website PoliticsHome.com.

In what is expected to be one of his toughest weeks yet, Brown is expected to show his support for the rights of millions more mothers to request flexible working hours as Labour attempts to pick itself up after its disastrous showing in the local elections.

A government review by Sainsbury's human resources director Imelda Walsh will recommend that millions of working mothers should gain the right to demand flexible hours. At present only mothers of children up to the age of six, those caring for elderly relatives or those whose child has a disability are entitled to make such a request.

Walsh will suggest that the current age limit should be at least doubled to include children up to 12, giving new rights to a least 2.6 million parents. Her recommendations are expected to be 'warmly' received by Downing Street.

Later this week the Prime Minister is expected to announce a draft legislative programme for the next parliamentary session, foreshadowing the Queen's Speech in the autumn.

But the scale of the downturn in his personal reputation with voters will further swell mounting anxiety among Labour MPs and ministers, especially those defending marginal seats. It is bound to amplify concerns that Brown lacks the presentational skills and leadership qualities to turn round the government's fortunes. There is speculation about a challenge to his leadership as Labour backbenchers reel from the impact of their party's massacre in the local elections and the fear of losing the Crewe and Nantwich by-election to a resurgent Tory party on 22 May.

Based on internet responses from a 5,000-strong panel taken over the past five days, the survey shows that Brown's overall satisfaction rating has crashed to minus 55 per cent. Fewer than a quarter of voters now think he is the best person to be in Number 10. And 43 per cent choose Cameron as best Prime Minister against just 23 per cent for Brown.

The panel was also asked to say what sort of government they would prefer if forced to choose between a Brown-led government and a Cameron one. This is often a better predictor than party shares of the outcome of general elections. A Tory government is preferred to a Labour one by a margin of 50 to 32 per cent. There are more voters who think the Conservatives would do a better job of governing than there are voters who think they would do a worse job.

In every key leadership category, Brown is now seen less favourably than his rival. Cameron is seen as more caring, competent, decisive, effective, fair, forward-looking, in touch with normal people, intelligent, likeable and moderate. He is also rated as stronger, more reliable and more trustworthy.

More damage was done to Brown's leadership last night as John Prescott revealed in his memoirs that he had urged Tony Blair to sack his Chancellor, but that Blair was 'scared' of him. The former Deputy Prime Minister described Brown as 'annoying, bewildering and prickly'.

Brown is also fighting demands for Scottish independence, and last night said: 'I will do whatever is necessary to ensure the stability and maintenance of the Union.' The Prime Minister called for pro-Union parties, together with business and trade unions, to form an alliance to prevent the breakup of the UK.